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#include <ulmblas.h>
#include <stdio.h>
#include <immintrin.h>
#define MC 384
#define KC 384
#define NC 4096
#define MR 8
#define NR 4
//
// Local buffers for storing panels from A, B and C
//
static double _A[MC*KC] __attribute__ ((aligned (32)));
static double _B[KC*NC] __attribute__ ((aligned (32)));
static double _C[MR*NR] __attribute__ ((aligned (32)));
//
// Packing complete panels from A (i.e. without padding)
//
static void
pack_MRxk(int k, const double *A, int incRowA, int incColA,
double *buffer)
{
int i, j;
for (j=0; j<k; ++j) {
for (i=0; i<MR; ++i) {
buffer[i] = A[i*incRowA];
}
buffer += MR;
A += incColA;
}
}
//
// Packing panels from A with padding if required
//
static void
pack_A(int mc, int kc, const double *A, int incRowA, int incColA,
double *buffer)
{
int mp = mc / MR;
int _mr = mc % MR;
int i, j;
for (i=0; i<mp; ++i) {
pack_MRxk(kc, A, incRowA, incColA, buffer);
buffer += kc*MR;
A += MR*incRowA;
}
if (_mr>0) {
for (j=0; j<kc; ++j) {
for (i=0; i<_mr; ++i) {
buffer[i] = A[i*incRowA];
}
for (i=_mr; i<MR; ++i) {
buffer[i] = 0.0;
}
buffer += MR;
A += incColA;
}
}
}
//
// Packing complete panels from B (i.e. without padding)
//
static void
pack_kxNR(int k, const double *B, int incRowB, int incColB,
double *buffer)
{
int i, j;
for (i=0; i<k; ++i) {
for (j=0; j<NR; ++j) {
buffer[j] = B[j*incColB];
}
buffer += NR;
B += incRowB;
}
}
//
// Packing panels from B with padding if required
//
static void
pack_B(int kc, int nc, const double *B, int incRowB, int incColB,
double *buffer)
{
int np = nc / NR;
int _nr = nc % NR;
int i, j;
for (j=0; j<np; ++j) {
pack_kxNR(kc, B, incRowB, incColB, buffer);
buffer += kc*NR;
B += NR*incColB;
}
if (_nr>0) {
for (i=0; i<kc; ++i) {
for (j=0; j<_nr; ++j) {
buffer[j] = B[j*incColB];
}
for (j=_nr; j<NR; ++j) {
buffer[j] = 0.0;
}
buffer += NR;
B += incRowB;
}
}
}
//
// Micro kernel for multiplying panels from A and B.
//
static void
dgemm_micro_kernel(int kc,
double alpha, const double *A, const double *B,
double beta,
double *C, int incRowC, int incColC)
{
double AB[MR*NR] __attribute__ ((aligned (32)));
// Cols of AB in SSE registers
__m256d ab_00_10_20_30, ab_40_50_60_70;
__m256d ab_01_11_21_31, ab_41_51_61_71;
__m256d ab_02_12_22_32, ab_42_52_62_72;
__m256d ab_03_13_23_33, ab_43_53_63_73;
__m256d a_0123, a_4567;
__m256d b_0000, b_1111, b_2222, b_3333;
__m256d tmp1, tmp2;
int i, j, l;
ab_00_10_20_30 = _mm256_setzero_pd(); ab_40_50_60_70 = _mm256_setzero_pd();
ab_01_11_21_31 = _mm256_setzero_pd(); ab_41_51_61_71 = _mm256_setzero_pd();
ab_02_12_22_32 = _mm256_setzero_pd(); ab_42_52_62_72 = _mm256_setzero_pd();
ab_03_13_23_33 = _mm256_setzero_pd(); ab_43_53_63_73 = _mm256_setzero_pd();
//
// Compute AB = A*B
//
for (l=0; l<kc; ++l) {
a_0123 = _mm256_load_pd(A);
a_4567 = _mm256_load_pd(A+4);
b_0000 = _mm256_broadcast_sd(B);
b_1111 = _mm256_broadcast_sd(B+1);
b_2222 = _mm256_broadcast_sd(B+2);
b_3333 = _mm256_broadcast_sd(B+3);
// col 0 of AB
tmp1 = a_0123;
tmp2 = a_4567;
tmp1 = _mm256_mul_pd(tmp1, b_0000);
tmp2 = _mm256_mul_pd(tmp2, b_0000);
ab_00_10_20_30 = _mm256_add_pd(tmp1, ab_00_10_20_30);
ab_40_50_60_70 = _mm256_add_pd(tmp2, ab_40_50_60_70);
// col 1 of AB
tmp1 = a_0123;
tmp2 = a_4567;
tmp1 = _mm256_mul_pd(tmp1, b_1111);
tmp2 = _mm256_mul_pd(tmp2, b_1111);
ab_01_11_21_31 = _mm256_add_pd(tmp1, ab_01_11_21_31);
ab_41_51_61_71 = _mm256_add_pd(tmp2, ab_41_51_61_71);
// col 2 of AB
tmp1 = a_0123;
tmp2 = a_4567;
tmp1 = _mm256_mul_pd(tmp1, b_2222);
tmp2 = _mm256_mul_pd(tmp2, b_2222);
ab_02_12_22_32 = _mm256_add_pd(tmp1, ab_02_12_22_32);
ab_42_52_62_72 = _mm256_add_pd(tmp2, ab_42_52_62_72);
// col 3 of AB
tmp1 = a_0123;
tmp2 = a_4567;
tmp1 = _mm256_mul_pd(tmp1, b_3333);
tmp2 = _mm256_mul_pd(tmp2, b_3333);
ab_03_13_23_33 = _mm256_add_pd(tmp1, ab_03_13_23_33);
ab_43_53_63_73 = _mm256_add_pd(tmp2, ab_43_53_63_73);
A += 8;
B += 4;
}
_mm256_store_pd(AB+ 0, ab_00_10_20_30);
_mm256_store_pd(AB+ 4, ab_40_50_60_70);
_mm256_store_pd(AB+ 8, ab_01_11_21_31);
_mm256_store_pd(AB+12, ab_41_51_61_71);
_mm256_store_pd(AB+16, ab_02_12_22_32);
_mm256_store_pd(AB+20, ab_42_52_62_72);
_mm256_store_pd(AB+24, ab_03_13_23_33);
_mm256_store_pd(AB+28, ab_43_53_63_73);
//
// Update C <- beta*C
//
if (beta==0.0) {
for (j=0; j<NR; ++j) {
for (i=0; i<MR; ++i) {
C[i*incRowC+j*incColC] = 0.0;
}
}
} else if (beta!=1.0) {
for (j=0; j<NR; ++j) {
for (i=0; i<MR; ++i) {
C[i*incRowC+j*incColC] *= beta;
}
}
}
//
// Update C <- C + alpha*AB (note: the case alpha==0.0 was already treated in
// the above layer dgemm_nn)
//
if (alpha==1.0) {
for (j=0; j<NR; ++j) {
for (i=0; i<MR; ++i) {
C[i*incRowC+j*incColC] += AB[i+j*MR];
}
}
} else {
for (j=0; j<NR; ++j) {
for (i=0; i<MR; ++i) {
C[i*incRowC+j*incColC] += alpha*AB[i+j*MR];
}
}
}
}
//
// Compute Y += alpha*X
//
static void
dgeaxpy(int m,
int n,
double alpha,
const double *X,
int incRowX,
int incColX,
double *Y,
int incRowY,
int incColY)
{
int i, j;
if (alpha!=1.0) {
for (j=0; j<n; ++j) {
for (i=0; i<m; ++i) {
Y[i*incRowY+j*incColY] += alpha*X[i*incRowX+j*incColX];
}
}
} else {
for (j=0; j<n; ++j) {
for (i=0; i<m; ++i) {
Y[i*incRowY+j*incColY] += X[i*incRowX+j*incColX];
}
}
}
}
//
// Compute X *= alpha
//
static void
dgescal(int m,
int n,
double alpha,
double *X,
int incRowX,
int incColX)
{
int i, j;
if (alpha!=0.0) {
for (j=0; j<n; ++j) {
for (i=0; i<m; ++i) {
X[i*incRowX+j*incColX] *= alpha;
}
}
} else {
for (j=0; j<n; ++j) {
for (i=0; i<m; ++i) {
X[i*incRowX+j*incColX] = 0.0;
}
}
}
}
//
// Macro Kernel for the multiplication of blocks of A and B. We assume that
// these blocks were previously packed to buffers _A and _B.
//
static void
dgemm_macro_kernel(int mc,
int nc,
int kc,
double alpha,
double beta,
double *C,
int incRowC,
int incColC)
{
int mp = (mc+MR-1) / MR;
int np = (nc+NR-1) / NR;
int _mr = mc % MR;
int _nr = nc % NR;
int mr, nr;
int i, j;
for (j=0; j<np; ++j) {
nr = (j!=np-1 || _nr==0) ? NR : _nr;
for (i=0; i<mp; ++i) {
mr = (i!=mp-1 || _mr==0) ? MR : _mr;
if (mr==MR && nr==NR) {
dgemm_micro_kernel(kc, alpha, &_A[i*kc*MR], &_B[j*kc*NR],
beta,
&C[i*MR*incRowC+j*NR*incColC],
incRowC, incColC);
} else {
dgemm_micro_kernel(kc, alpha, &_A[i*kc*MR], &_B[j*kc*NR],
0.0,
_C, 1, MR);
dgescal(mr, nr, beta,
&C[i*MR*incRowC+j*NR*incColC], incRowC, incColC);
dgeaxpy(mr, nr, 1.0, _C, 1, MR,
&C[i*MR*incRowC+j*NR*incColC], incRowC, incColC);
}
}
}
}
//
// Compute C <- beta*C + alpha*A*B
//
void
dgemm_nn(int m,
int n,
int k,
double alpha,
const double *A,
int incRowA,
int incColA,
const double *B,
int incRowB,
int incColB,
double beta,
double *C,
int incRowC,
int incColC)
{
int mb = (m+MC-1) / MC;
int nb = (n+NC-1) / NC;
int kb = (k+KC-1) / KC;
int _mc = m % MC;
int _nc = n % NC;
int _kc = k % KC;
int mc, nc, kc;
int i, j, l;
double _beta;
if (alpha==0.0 || k==0) {
dgescal(m, n, beta, C, incRowC, incColC);
return;
}
for (j=0; j<nb; ++j) {
nc = (j!=nb-1 || _nc==0) ? NC : _nc;
for (l=0; l<kb; ++l) {
kc = (l!=kb-1 || _kc==0) ? KC : _kc;
_beta = (l==0) ? beta : 1.0;
pack_B(kc, nc,
&B[l*KC*incRowB+j*NC*incColB], incRowB, incColB,
_B);
for (i=0; i<mb; ++i) {
mc = (i!=mb-1 || _mc==0) ? MC : _mc;
pack_A(mc, kc,
&A[i*MC*incRowA+l*KC*incColA], incRowA, incColA,
_A);
dgemm_macro_kernel(mc, nc, kc, alpha, _beta,
&C[i*MC*incRowC+j*NC*incColC],
incRowC, incColC);
}
}
}
}
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